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In how many shortest ways can we reach f...

In how many shortest ways can we reach from the point (0, 0, 0) to point (3, 7, 11) in space where the movement is possible only along het x-axis, y-axis, and z-axis or parallel to them and change of axes is permitted only at integral points. (An integral point is one, which has its coordinate as integer.)

Text Solution

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The correct Answer is:
`.^(21)C_(3)xx .^(18)C_(7)`
The total number of units to be covered is 3+7+11=21. A person can choose 3 units in `.^(21)C_(3)` ways. A person can choose 7 units from remaining 18 in `.^(18)C_(7)` ways. The rest 11 units can be chosen in 1 way.
Therefore, the total number of ways is `.^(21)C_(3)xx .^(18)C_(7)xx1`.
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